A067279 - OEIS

%I #10 Sep 08 2022 08:45:05

%S 1,1,0,3,2,2,2,3,6,6,8,1,11,12,7,6,13,7,3,2,2,2,9,20,9,16,11,0,12,13,

%T 19,25,26,31,18,24,21,32,12,34,22,24,13,14,41,20,34,29,22,40,50,4,33,

%U 50,39,8,15,24,14,59,40,3,9,29,27,14,18,39,59,44,28,30,35,5,64,20,18

%N Factorial expansion of zeta(2) : zeta(2) = Sum_{n>=1} a(n)/n!.

%H G. C. Greubel, <a href="/A067279/b067279.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = floor(n!*zeta(2)) - n*floor((n-1)!*zeta(2)), for n>=2.

%t With[{b = Zeta[2]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* _G. C. Greubel_, Nov 26 2018 *)

%o (PARI) default(realprecision, 250); b = zeta(2); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", ")) \\ _G. C. Greubel_, Nov 26 2018

%o (Magma) SetDefaultRealField(RealField(250)); L:=RiemannZeta(); [Floor(Evaluate(L,2))] cat [Floor(Factorial(n)*Evaluate(L,2)) - n*Floor(Factorial((n-1))*Evaluate(L,2)) : n in [2..80]]; // _G. C. Greubel_, Nov 26 2018

%o (Sage)

%o def A067279(n):

%o     if (n==1): return floor(zeta(2))

%o     else: return expand(floor(factorial(n)*zeta(2)) - n*floor(factorial(n-1)*zeta(2)))

%o [A067279(n) for n in (1..80)] # _G. C. Greubel_, Nov 26 2018

%Y Cf. A067277 (zeta(3)), A068447 (zeta(4)), A068454 (zeta(5)), A068455 (zeta(6)), A068456 (zeta(7)), A068457 (zeta(8)), A068458 (zeta(9)), A068459 (zeta(10)).

%K easy,nonn

%O 1,4

%A _Benoit Cloitre_, Mar 10 2002

%E a(1) corrected by _G. C. Greubel_, Nov 26 2018